How can I create a single Cycles texture with a different image for each object it's assigned to?
You can use a node group for your settings. The texture is an input to the node group but all other settings are hardcoded into it. Go into the node editor with a material you want to reuse. Select the nodes you want to make common (for instance, hold down shift while selecting). Press Ctrl - G to make them a group. You are now seeing the internals of your group. Press tab to close it. Press tab again to edit it. It is sort of edit mode for node groups. It looks like this:



To the left you see inputs and to the right outputs. There are empty circles on the input and output nodes. Drag from or to these to add more parameters. There is also an editor for this to the right in the properties panel. Here you can add, remove, reorder and rename parameters.

If you tab out you can rename your group.

Now that you have your group. You can use it in other materials. When adding a node in the node editor, your group will show up under groups.



Here I have used my SimpleMaterial on two cubes. One of them got a checkered texture for color and the other got a solid color: